I would say absolutely NO don't send the mail. That will undermine her authority and position in her bosses eyes. Put yourself in her shoes and then think how you would feel about her mailing your boss to ask him to take it easy on you. It's like a letter from your mum.
Speak to her about it and see if she wants you to send something…
She has to deal with the situation and your job is to support her, not to get involved in it at work.
She should stand by her guns, either systems get fixed (shouldn't IT do that?) or she goes to a meeting. Can't have both and she has to state that in a black and white way. Leave no ambiguity.
I hope it all gets sorted out in a way that everyone is happy. Best to clear the air both at home and at work before anyone is in the situation where a breakdown of any kind is on the cards